A 30 vector field given by V = 4ryi +3y²j +-k, represents the flow of water in a system. Use Gauss's theorem to find the overall flow of water out of a section of a cylinder shown in the figure below, which is described bysos 2x and has a radius of 2m and height of dm. -2m A- 4 m a) Find the divergence of the vector field V. div(V) -[ 10y-1 ] 10y – 1 b) Convert your divergence to cylindrical coordinates, and find the total flow out of the container using Gauss's Theorem. f h, V •ndS = c) Which of the following provides the best interpretation of the result: O The cylinder is a source for water O The cylinder is a sink for water O The cylinder is neither a source nor a sink.
A 30 vector field given by V = 4ryi +3y²j +-k, represents the flow of water in a system. Use Gauss's theorem to find the overall flow of water out of a section of a cylinder shown in the figure below, which is described bysos 2x and has a radius of 2m and height of dm. -2m A- 4 m a) Find the divergence of the vector field V. div(V) -[ 10y-1 ] 10y – 1 b) Convert your divergence to cylindrical coordinates, and find the total flow out of the container using Gauss's Theorem. f h, V •ndS = c) Which of the following provides the best interpretation of the result: O The cylinder is a source for water O The cylinder is a sink for water O The cylinder is neither a source nor a sink.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![A 30 vector field given by V = 4ryi +3y²j +-k, represents the flow of water in a system. Use Gauss's theorem to find the overall flow of water
out of a section of a cylinder shown in the figure below, which is described bysos 2x and has a radius of 2m and height of dm.
-2m
A- 4 m
a) Find the divergence of the vector field V.
div(V) -[ 10y-1 ] 10y – 1
b) Convert your divergence to cylindrical coordinates, and find the total flow out of the container using Gauss's Theorem.
f h, V •ndS =
c) Which of the following provides the best interpretation of the result:
O The cylinder is a source for water
O The cylinder is a sink for water
O The cylinder is neither a source nor a sink.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe37ebe49-731c-47f9-a49b-3a5f656faaa2%2Fe4d0a17e-bf51-48b4-aeee-d7c37a2e9868%2Fbprqtg7_processed.png&w=3840&q=75)
Transcribed Image Text:A 30 vector field given by V = 4ryi +3y²j +-k, represents the flow of water in a system. Use Gauss's theorem to find the overall flow of water
out of a section of a cylinder shown in the figure below, which is described bysos 2x and has a radius of 2m and height of dm.
-2m
A- 4 m
a) Find the divergence of the vector field V.
div(V) -[ 10y-1 ] 10y – 1
b) Convert your divergence to cylindrical coordinates, and find the total flow out of the container using Gauss's Theorem.
f h, V •ndS =
c) Which of the following provides the best interpretation of the result:
O The cylinder is a source for water
O The cylinder is a sink for water
O The cylinder is neither a source nor a sink.
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